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arXiv · 2403.08620

Demailly-Lelong numbers on complex spaces

Chung-Ming Pan
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Abstract

We prove a conjecture proposed by Berman-Boucksom-Eyssidieux-Guedj-Zeriahi, affirming that the Demailly-Lelong number can be determined through a combination of intersection numbers given by the divisorial part of the potential and the SNC divisors over a log resolution of the maximal ideal of a given point. Moreover, this result establishes a pointwise comparison of two different notions of Lelong numbers of plurisubharmonic functions defined on singular complex spaces. We also provide an estimate for quotient singularities and sharp estimates for two-dimensional ADE singularities.

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Chung-Ming Pan. 2024-03-13. Demailly-Lelong numbers on complex spaces. https://doi.org/10.1007/s00209-024-03636-z

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